Peer-Reviewed journal indexed by Mathematical Reviews and Zentralblatt MATH.

# Metallic structure on Lagrangian manifold

Metallic structure on Lagrangian manifold

Author

Geeta Verma

Abstract

In this paper, the author convention with the Lagrange vertical structure on the vertical space TV (E) endowed with a non null (1,1) tensor field FV satisfying metallic structure F2 − αF − βI = 0. The horizontal subspace TH(E) is applied on the same structure. Next, some theorems are proved and obtained conditions under which the distribution L and M are ∇-parallel, ¯∇ anti half parallel when ∇ = ¯∇. Lastly, certain theorems on geodesics on the Lagrange manifold are deduced.

Keywords: Metallic structure; Lagrangian manifold; vertical space.